Vectors Question

[shinny]

This is probably going to turn out to be a very stupid thread and question but meh I'll get on to it.

To prove that the quadrilateral ABCD is a rhombus, it is sufficient to show that;
The answer is and

Thing I was wondering though was, doesn't the former imply the latter? It didn't specify unit vectors or anything, so isn't proving by itself enough? For two vectors to equal each other, that already implies they're equal in direction AND length no?

[Pandemonium]

i thought ab-> = dc-> and |AB| = |AD| would've been better proof.

[shinny]

Oh hang on a sec, I misread the answer <_< Yeh they had AB=DC and |AB|=|DC| sorry ahah

[kj_]

This question seems dodgy to me - I was discussing it with a friend of mine a few weeks ago:

For ABCD to be a rhombus, assuming that you're labeling the verticies in a clockwise manner, wouldn't you also have to prove |AB| = |BC|?

Maybe there was a typo in the solution, and they really meant you have to prove |AB| = |BC| and not |AB| = |DC|, because what you say is correct

[shinny]

yehyeh dw ahah, misread the answer. They did it properly for this exam. Geometry>me